Question

Find the equation, in vertex form, for a parabola with a vertex of (2,-5) that goes through the point (3,4).

Answer 1

Y=9(x−2)²−5 is the solution

Explanation in full below

Using the vertex co-ordinates we can deduct the formula
y=a(x-2)²-5 

using the co-ordinate (3,4), use x=3, y=4 to find a

y=a(x-2)²-5 
4=a(3-2)² -5
4=a(1)²-5
4=a-5
a=9

Subsituting a into the first equation
y=a(x-2)²-5 
y=9(x-2)²-5 

The solution is y=9(x-2)²-5